December, 2024 Hausdorff dimension of sets with restricted, slowly growing partial quotients in semi-regular continued fractions
Yuto NAKAJIMA, Hiroki TAKAHASI
Author Affiliations +
J. Math. Soc. Japan Advance Publication 1-14 (December, 2024). DOI: 10.2969/jmsj/93059305

Abstract

We determine the Hausdorff dimension of sets of irrationals in (0,1) whose partial quotients in semi-regular continued fractions obey certain restrictions and growth conditions. This result substantially generalizes that of the second author [Proc. Amer. Math. Soc., 151 (2023), 3645–3653] and the solution of Hirst's conjecture [B.-W. Wang and J. Wu, Bull. London Math. Soc., 40 (2008), 18–22], both previously obtained for the regular continued fraction. To prove the result, we construct non-autonomous iterated function systems well-adapted to the given restrictions and growth conditions on partial quotients, estimate the associated pressure functions, and then apply Bowen's formula.

Funding Statement

The second named author was partially supported by the JSPS KAKENHI 23K20220.

Citation

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Yuto NAKAJIMA. Hiroki TAKAHASI. "Hausdorff dimension of sets with restricted, slowly growing partial quotients in semi-regular continued fractions." J. Math. Soc. Japan Advance Publication 1 - 14, December, 2024. https://doi.org/10.2969/jmsj/93059305

Information

Received: 24 February 2024; Published: December, 2024
First available in Project Euclid: 17 December 2024

Digital Object Identifier: 10.2969/jmsj/93059305

Subjects:
Primary: 11A55
Secondary: 37C45 , 37C60

Keywords: continued fractions , Hausdorff dimension , iterated function system (IFS)

Rights: Copyright ©2024 Mathematical Society of Japan

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